# Calculating Vrms from a given function

#### blalaw

Joined Oct 28, 2013
9
I need to calculate the effective RMS values given
a) g(t) = 2 + 3cos(100t) + 4cos(100t - 120)
b) h(t) = 2 + 3cos(100t) + 4cos(101t - 120)

I am pretty sure the first one is straight forward since 2 is a constant voltage then the value will just be two the second part would be 3/sqrt(2) and the last part would be 4/sqrt(2) in phase -120 degrees and just add them up if that is correct I believe.

The second part I am kind of lost because I am not sure what to do with the 101t since it is not the same as the 100t.

#### The Electrician

Joined Oct 9, 2007
2,778
I need to calculate the effective RMS values given
a) g(t) = 2 + 3cos(100t) + 4cos(100t - 120)
b) h(t) = 2 + 3cos(100t) + 4cos(101t - 120)

I am pretty sure the first one is straight forward since 2 is a constant voltage then the value will just be two the second part would be 3/sqrt(2) and the last part would be 4/sqrt(2) in phase -120 degrees and just add them up if that is correct I believe.

The second part I am kind of lost because I am not sure what to do with the 101t since it is not the same as the 100t.
What result do you get for the first part after you add them up?

#### WBahn

Joined Mar 31, 2012
25,745
Ask yourself if the method you are trying to use makes sense in the limiting cases.

For instance, what if you have

v(t) = 3V cos(ωt) + 4V cos(ωt + 180°)

Or what if you have

v(t) = 3V cos(ωt) + 4V cos(ωt + 0°)